Non-linear Kinetic Characteristics Of The Shallow Reticulated Spherical Shell With Stationary Load And Dynamic Load

In this paper, nonlinear mechanical behavior of the three-dimensional shallow reticulated spherical shell was studied. The domestic and foreign present state of the shallow reticulated spherical shell was introduced. Analysis and calculation of the shallow reticulated spherical shell in the aspects of static and static with dynamic were studied systematically. According to the nonlinear dynamical theory of plate and shell, modern mathematical analytic method of nonlinear dynamic and ideology of continuous quasi-shell method were used to convert reticulated shell to continuous shell. Nonlinear dynamical governing equations were established and boundary conditions and initial conditions were determined appropriately. The nonlinear bending problem of the shallow reticulated spherical shell, dynamical stability problem of the shallow reticulated spherical shell, bifurcation problem and chaos problem of the shallow reticulated spherical shell were analyzed.At first, significance of the study on reticulated shells, bifurcation and chaos were introduced. Then, domestic and foreign developing status of the study on reticulated shells was introduced.The nonlinear bending problem of shallow reticulated spherical shell was studied consequently. The equations of shallow spherical reticulated shell were obtained by adding the equations of middle cross section of the three-dimensional reticulated frame and initial deflection to the equations of three-dimensional reticulated frame. Under the boundary conditions of fixing and clamping, the nonlinear bending problems of the three-dimensional shallow spherical reticulated shell objected even load were solved by the method of modified iteration. The quadratic approximate analytic solution with much higher accuracy was clearly presented oThe problem of the nonlinear dynamical stability of the shallow reticulated spherical shell under the load of both dynamic and static was analyzed. Due to nonlinear dynamical variation equations and compatible equations of the shallow reticulated conical shell, a nonlinear differential equation with quadric items was obtained by the Galerkin method under the fixed edges boundary condition. In order to discuss chaos motion, a kind of nonlinear dynamical free oscillation equation was solved. The problem of statistic at the equilibrium point of the system was discussed using exponent Floquet. Accurate solution to the free oscillation equation of the shallow reticulated spherical shell was obtained. Then Melnikov function was solved,critical condition of chaos motion was given and the existence of chaos motion was confirmed through the digital simulation phase plans and the Poincare map too.